The data fusion of low spatial-resolution hyperspectral and high spatial-resolution multispectral images enables the production of high spatial-resolution hyperspectral data with small spectral distortion. EO-1/Hyperion is the world's first hyperspectral sensor. It was launched in 2001 and has a similar orbit to Terra/ASTER. In this work, we apply hyperspectral and multispectral data fusion to EO-1/Hyperion and Terra/ASTER datasets by the preprocessing of datasets and the onboard cross-calibration of sensor characteristics. The relationship of the spectral response function is determined by convex optimization by comparing hyperspectral and multispectral images over the same spectral range. After accurate image registration, the relationship of the point spread function is obtained by estimating a matrix that acts as Gaussian blur filter between two images. Two pansharpening-based methods and one unmixing-based method are adopted for hyperspectral and multispectral data fusion and their properties are investigated.